Paper 4: Fundamentals of Business Mathematics & Statistic

2.16 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Solution :

4(x + 1) < 2x + 3

4x +4 < 2x + 3

4x + 4 – 2x -4 < 2x + 3 – 2x – 4

2x < -1

2x 1

2 2

<−

x^1

2

<−

Example 20 :

Solve the inequality -2(m – 3) < 5 (m+1) - 12

Solution :

• 2(m – 3) < 5 (m + 1) - 12


• 2m + 6 < 5m + 5 – 12


• 7m < - 13
  m^13

  
  

  7
  Example 21 :
  Solve the inequality 2(1 – x) + 5 ≤ 3 (2x – 1)
  Solution :
  2(1 – x) + 5 ≤ 3 (2x – 1)
  2 – 2x + 5 ≤ 6x – 3
  10 ≤ 8x

  
  

  
  

(^10) x
8 ≤
(^5) x
4 ≤
Now, with this inequality we ended up with the variable on the right side when it more traditionally on the
left side. So, let’s switch things around to get the variable onto the left side. Note however, that we’re
going to need also switch the direction of the inequality to make sure that we don’t change the answer.
So, here is the inequality notation for the inequality.
x^5
≥ 4
Now, let’s solve some double inequalities. The process here is similar in some ways to solving single inequalities
and yet very different in other ways. Since there are two inequalities there isn’t any way to get the variables
on “one side” of the inequality and the numbers on the other. It is easier to see how these work if we do an
example or two so let’s do that.
Example 22 :
Solve the inequality – 6 ≤ 2(x – 5) < 7
Solution :

• 6 ≤ 2(x – 5) < 7